%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : REL026+4 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:24:55 AM UTC 2026
% Result : Theorem 13.17s 12.11s
% Output : CNFRefutation 13.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 13
% Syntax : Number of formulae : 136 ( 119 unt; 0 def)
% Number of atoms : 157 ( 156 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 56 ( 35 ~; 15 |; 4 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 193 ( 4 sgn 26 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(maddux1_join_commutativity,axiom,
! [X0,X1] : join(X0,X1) = join(X1,X0),
file('theBenchmark.p',maddux1_join_commutativity) ).
fof(maddux2_join_associativity,axiom,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
file('theBenchmark.p',maddux2_join_associativity) ).
fof(maddux3_a_kind_of_de_Morgan,axiom,
! [X0,X1] : X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),
file('theBenchmark.p',maddux3_a_kind_of_de_Morgan) ).
fof(maddux4_definiton_of_meet,axiom,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X0),complement(X1))),
file('theBenchmark.p',maddux4_definiton_of_meet) ).
fof(composition_identity,axiom,
! [X0] : composition(X0,one) = X0,
file('theBenchmark.p',composition_identity) ).
fof(composition_distributivity,axiom,
! [X0,X1,X2] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
file('theBenchmark.p',composition_distributivity) ).
fof(converse_idempotence,axiom,
! [X0] : converse(converse(X0)) = X0,
file('theBenchmark.p',converse_idempotence) ).
fof(converse_additivity,axiom,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
file('theBenchmark.p',converse_additivity) ).
fof(converse_multiplicativity,axiom,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
file('theBenchmark.p',converse_multiplicativity) ).
fof(converse_cancellativity,axiom,
! [X0,X1] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
file('theBenchmark.p',converse_cancellativity) ).
fof(def_top,axiom,
! [X0] : top = join(X0,complement(X0)),
file('theBenchmark.p',def_top) ).
fof(def_zero,axiom,
! [X0] : zero = meet(X0,complement(X0)),
file('theBenchmark.p',def_zero) ).
fof(goals,conjecture,
! [X0,X1] :
( join(X0,one) = one
=> ( join(composition(X0,X1),meet(composition(X0,top),X1)) = meet(composition(X0,top),X1)
& join(meet(composition(X0,top),X1),composition(X0,X1)) = composition(X0,X1) ) ),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0,X1] :
( join(X0,one) = one
=> ( join(composition(X0,X1),meet(composition(X0,top),X1)) = meet(composition(X0,top),X1)
& join(meet(composition(X0,top),X1),composition(X0,X1)) = composition(X0,X1) ) ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_18,plain,
join(A,B) = join(B,A),
inference(clausify,[status(thm)],[maddux1_join_commutativity]) ).
cnf(c_19,plain,
join(join(A,B),C) = join(A,join(B,C)),
inference(clausify,[status(thm)],[maddux2_join_associativity]) ).
cnf(c_20,plain,
join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) = A,
inference(clausify,[status(thm)],[maddux3_a_kind_of_de_Morgan]) ).
cnf(c_21,plain,
join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = A,
inference(paramod,[status(thm)],[c_18,c_20]) ).
cnf(c_22,plain,
meet(A,B) = complement(join(complement(A),complement(B))),
inference(clausify,[status(thm)],[maddux4_definiton_of_meet]) ).
cnf(c_24,plain,
composition(A,one) = A,
inference(clausify,[status(thm)],[composition_identity]) ).
cnf(c_25,plain,
composition(join(A,B),C) = join(composition(A,C),composition(B,C)),
inference(clausify,[status(thm)],[composition_distributivity]) ).
cnf(c_26,plain,
converse(converse(A)) = A,
inference(clausify,[status(thm)],[converse_idempotence]) ).
cnf(c_27,plain,
converse(join(A,B)) = join(converse(A),converse(B)),
inference(clausify,[status(thm)],[converse_additivity]) ).
cnf(c_28,plain,
converse(composition(A,B)) = composition(converse(B),converse(A)),
inference(clausify,[status(thm)],[converse_multiplicativity]) ).
cnf(c_29,plain,
complement(A) = join(composition(converse(B),complement(composition(B,A))),complement(A)),
inference(clausify,[status(thm)],[converse_cancellativity]) ).
cnf(c_2703,plain,
complement(A) = join(complement(A),composition(converse(B),complement(composition(B,A)))),
inference(paramod,[status(thm)],[c_18,c_29]) ).
cnf(c_30,plain,
join(complement(A),composition(converse(B),complement(composition(B,A)))) = complement(A),
inference(copy,[status(thm)],[c_2703]) ).
cnf(c_31,plain,
join(A,complement(A)) = top,
inference(clausify,[status(thm)],[def_top]) ).
cnf(c_32,plain,
meet(A,complement(A)) = zero,
inference(clausify,[status(thm)],[def_zero]) ).
cnf(c_2704,plain,
complement(join(complement(A),complement(complement(A)))) = zero,
inference(paramod,[status(thm)],[c_22,c_32]) ).
cnf(c_33,plain,
complement(top) = zero,
inference(paramod,[status(thm)],[c_31,c_2704]) ).
fof(nnf_17,plain,
? [X0,X1] :
( ( meet(composition(X0,top),X1) != join(composition(X0,X1),meet(composition(X0,top),X1))
| composition(X0,X1) != join(meet(composition(X0,top),X1),composition(X0,X1)) )
& join(X0,one) = one ),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
( ( meet(composition(sK0,top),sK1) != join(composition(sK0,sK1),meet(composition(sK0,top),sK1))
| composition(sK0,sK1) != join(meet(composition(sK0,top),sK1),composition(sK0,sK1)) )
& join(sK0,one) = one ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[nnf_17]) ).
cnf(c_40,negated_conjecture,
join(sK0,one) = one,
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_41,negated_conjecture,
join(one,sK0) = one,
inference(paramod,[status(thm)],[c_18,c_40]) ).
cnf(c_42,negated_conjecture,
( meet(composition(sK0,top),sK1) != join(composition(sK0,sK1),meet(composition(sK0,top),sK1))
| composition(sK0,sK1) != join(meet(composition(sK0,top),sK1),composition(sK0,sK1)) ),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_2705,negated_conjecture,
( meet(composition(sK0,top),sK1) != join(composition(sK0,sK1),meet(composition(sK0,top),sK1))
| composition(sK0,sK1) != join(complement(join(complement(composition(sK0,top)),complement(sK1))),composition(sK0,sK1)) ),
inference(paramod,[status(thm)],[c_22,c_42]) ).
cnf(c_2706,negated_conjecture,
( meet(composition(sK0,top),sK1) != join(composition(sK0,sK1),meet(composition(sK0,top),sK1))
| composition(sK0,sK1) != join(complement(join(complement(sK1),complement(composition(sK0,top)))),composition(sK0,sK1)) ),
inference(paramod,[status(thm)],[c_18,c_2705]) ).
cnf(c_2707,negated_conjecture,
( complement(join(complement(composition(sK0,top)),complement(sK1))) != join(composition(sK0,sK1),meet(composition(sK0,top),sK1))
| composition(sK0,sK1) != join(complement(join(complement(sK1),complement(composition(sK0,top)))),composition(sK0,sK1)) ),
inference(paramod,[status(thm)],[c_22,c_2706]) ).
cnf(c_2708,negated_conjecture,
( complement(join(complement(sK1),complement(composition(sK0,top)))) != join(composition(sK0,sK1),meet(composition(sK0,top),sK1))
| composition(sK0,sK1) != join(complement(join(complement(sK1),complement(composition(sK0,top)))),composition(sK0,sK1)) ),
inference(paramod,[status(thm)],[c_18,c_2707]) ).
cnf(c_2709,negated_conjecture,
( complement(join(complement(sK1),complement(composition(sK0,top)))) != join(composition(sK0,sK1),complement(join(complement(composition(sK0,top)),complement(sK1))))
| composition(sK0,sK1) != join(complement(join(complement(sK1),complement(composition(sK0,top)))),composition(sK0,sK1)) ),
inference(paramod,[status(thm)],[c_22,c_2708]) ).
cnf(c_2710,negated_conjecture,
( complement(join(complement(sK1),complement(composition(sK0,top)))) != join(composition(sK0,sK1),complement(join(complement(sK1),complement(composition(sK0,top)))))
| composition(sK0,sK1) != join(complement(join(complement(sK1),complement(composition(sK0,top)))),composition(sK0,sK1)) ),
inference(paramod,[status(thm)],[c_18,c_2709]) ).
cnf(c_2711,negated_conjecture,
( complement(join(complement(sK1),complement(composition(sK0,top)))) != join(complement(join(complement(sK1),complement(composition(sK0,top)))),composition(sK0,sK1))
| composition(sK0,sK1) != join(complement(join(complement(sK1),complement(composition(sK0,top)))),composition(sK0,sK1)) ),
inference(paramod,[status(thm)],[c_18,c_2710]) ).
cnf(c_2712,negated_conjecture,
( complement(join(complement(sK1),complement(composition(sK0,top)))) != join(complement(join(complement(sK1),complement(composition(sK0,top)))),composition(sK0,sK1))
| join(complement(join(complement(sK1),complement(composition(sK0,top)))),composition(sK0,sK1)) != composition(sK0,sK1) ),
inference(copy,[status(thm)],[c_2711]) ).
cnf(c_43,negated_conjecture,
( join(complement(join(complement(sK1),complement(composition(sK0,top)))),composition(sK0,sK1)) != complement(join(complement(sK1),complement(composition(sK0,top))))
| join(complement(join(complement(sK1),complement(composition(sK0,top)))),composition(sK0,sK1)) != composition(sK0,sK1) ),
inference(copy,[status(thm)],[c_2712]) ).
cnf(c_2713,plain,
join(join(A,B),C) = join(B,join(A,C)),
inference(paramod,[status(thm)],[c_18,c_19]) ).
cnf(c_45,plain,
join(A,join(B,C)) = join(B,join(A,C)),
inference(paramod,[status(thm)],[c_19,c_2713]) ).
cnf(c_46,plain,
join(complement(join(A,complement(B))),complement(join(complement(B),complement(A)))) = B,
inference(paramod,[status(thm)],[c_18,c_21]) ).
cnf(c_47,plain,
join(complement(join(complement(A),B)),complement(join(complement(B),complement(A)))) = A,
inference(paramod,[status(thm)],[c_18,c_21]) ).
cnf(c_2714,plain,
converse(A) = composition(converse(one),converse(A)),
inference(paramod,[status(thm)],[c_24,c_28]) ).
cnf(c_50,plain,
composition(converse(one),converse(A)) = converse(A),
inference(copy,[status(thm)],[c_2714]) ).
cnf(c_2715,plain,
converse(join(composition(A,B),composition(C,B))) = composition(converse(B),converse(join(A,C))),
inference(paramod,[status(thm)],[c_25,c_28]) ).
cnf(c_2716,plain,
join(converse(composition(A,B)),converse(composition(C,B))) = composition(converse(B),converse(join(A,C))),
inference(paramod,[status(thm)],[c_27,c_2715]) ).
cnf(c_2717,plain,
join(composition(converse(B),converse(A)),converse(composition(C,B))) = composition(converse(B),converse(join(A,C))),
inference(paramod,[status(thm)],[c_28,c_2716]) ).
cnf(c_2718,plain,
join(composition(converse(B),converse(A)),composition(converse(B),converse(C))) = composition(converse(B),converse(join(A,C))),
inference(paramod,[status(thm)],[c_28,c_2717]) ).
cnf(c_2719,plain,
join(composition(converse(B),converse(A)),composition(converse(B),converse(C))) = composition(converse(B),join(converse(A),converse(C))),
inference(paramod,[status(thm)],[c_27,c_2718]) ).
cnf(c_51,plain,
composition(converse(A),join(converse(B),converse(C))) = join(composition(converse(A),converse(B)),composition(converse(A),converse(C))),
inference(copy,[status(thm)],[c_2719]) ).
cnf(c_2720,plain,
join(complement(top),complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_31,c_21]) ).
cnf(c_57,plain,
join(zero,complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_33,c_2720]) ).
cnf(c_2721,plain,
join(complement(join(complement(A),complement(A))),complement(top)) = A,
inference(paramod,[status(thm)],[c_31,c_21]) ).
cnf(c_2722,plain,
join(complement(join(complement(A),complement(A))),zero) = A,
inference(paramod,[status(thm)],[c_33,c_2721]) ).
cnf(c_58,plain,
join(zero,complement(join(complement(A),complement(A)))) = A,
inference(paramod,[status(thm)],[c_18,c_2722]) ).
cnf(c_2723,plain,
composition(one,A) = join(composition(one,A),composition(sK0,A)),
inference(paramod,[status(thm)],[c_41,c_25]) ).
cnf(c_67,plain,
join(composition(one,A),composition(sK0,A)) = composition(one,A),
inference(copy,[status(thm)],[c_2723]) ).
cnf(c_2724,plain,
composition(converse(one),A) = converse(converse(A)),
inference(paramod,[status(thm)],[c_26,c_50]) ).
cnf(c_81,plain,
composition(converse(one),A) = A,
inference(paramod,[status(thm)],[c_26,c_2724]) ).
cnf(c_2725,plain,
one = converse(one),
inference(paramod,[status(thm)],[c_81,c_24]) ).
cnf(c_83,plain,
converse(one) = one,
inference(copy,[status(thm)],[c_2725]) ).
cnf(c_87,plain,
join(complement(A),complement(composition(one,A))) = complement(A),
inference(paramod,[status(thm)],[c_81,c_30]) ).
cnf(c_88,plain,
composition(one,A) = A,
inference(paramod,[status(thm)],[c_83,c_81]) ).
cnf(c_2726,plain,
join(A,composition(sK0,A)) = composition(one,A),
inference(paramod,[status(thm)],[c_88,c_67]) ).
cnf(c_90,plain,
join(A,composition(sK0,A)) = A,
inference(paramod,[status(thm)],[c_88,c_2726]) ).
cnf(c_91,plain,
join(complement(A),complement(A)) = complement(A),
inference(paramod,[status(thm)],[c_88,c_87]) ).
cnf(c_92,plain,
join(zero,complement(complement(A))) = A,
inference(paramod,[status(thm)],[c_91,c_58]) ).
cnf(c_2727,plain,
join(complement(join(complement(complement(A)),A)),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_31,c_47]) ).
cnf(c_2728,plain,
join(complement(join(A,complement(complement(A)))),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_18,c_2727]) ).
cnf(c_2729,plain,
join(complement(join(A,complement(complement(A)))),zero) = complement(A),
inference(paramod,[status(thm)],[c_33,c_2728]) ).
cnf(c_95,plain,
join(zero,complement(join(A,complement(complement(A))))) = complement(A),
inference(paramod,[status(thm)],[c_18,c_2729]) ).
cnf(c_96,plain,
complement(complement(A)) = A,
inference(paramod,[status(thm)],[c_95,c_57]) ).
cnf(c_97,plain,
join(zero,complement(join(A,A))) = complement(A),
inference(paramod,[status(thm)],[c_96,c_95]) ).
cnf(c_98,plain,
join(zero,A) = A,
inference(paramod,[status(thm)],[c_96,c_92]) ).
cnf(c_99,plain,
complement(join(A,A)) = complement(A),
inference(paramod,[status(thm)],[c_98,c_97]) ).
cnf(c_2730,plain,
join(A,B) = join(B,join(A,composition(sK0,B))),
inference(paramod,[status(thm)],[c_90,c_45]) ).
cnf(c_121,plain,
join(A,join(B,composition(sK0,A))) = join(B,A),
inference(copy,[status(thm)],[c_2730]) ).
cnf(c_2731,plain,
composition(A,join(converse(B),converse(C))) = join(composition(converse(converse(A)),converse(B)),composition(converse(converse(A)),converse(C))),
inference(paramod,[status(thm)],[c_26,c_51]) ).
cnf(c_2732,plain,
composition(A,join(converse(B),converse(C))) = join(composition(A,converse(B)),composition(converse(converse(A)),converse(C))),
inference(paramod,[status(thm)],[c_26,c_2731]) ).
cnf(c_123,plain,
composition(A,join(converse(B),converse(C))) = join(composition(A,converse(B)),composition(A,converse(C))),
inference(paramod,[status(thm)],[c_26,c_2732]) ).
cnf(c_2733,plain,
join(complement(join(A,B)),complement(join(complement(complement(A)),complement(B)))) = complement(A),
inference(paramod,[status(thm)],[c_96,c_21]) ).
cnf(c_137,plain,
join(complement(join(A,B)),complement(join(A,complement(B)))) = complement(A),
inference(paramod,[status(thm)],[c_96,c_2733]) ).
cnf(c_2734,plain,
join(complement(join(A,B)),complement(join(complement(complement(B)),complement(A)))) = complement(B),
inference(paramod,[status(thm)],[c_96,c_46]) ).
cnf(c_139,plain,
join(complement(join(A,B)),complement(join(B,complement(A)))) = complement(B),
inference(paramod,[status(thm)],[c_96,c_2734]) ).
cnf(c_2735,plain,
complement(complement(A)) = join(A,A),
inference(paramod,[status(thm)],[c_99,c_96]) ).
cnf(c_2736,plain,
A = join(A,A),
inference(paramod,[status(thm)],[c_96,c_2735]) ).
cnf(c_146,plain,
join(A,A) = A,
inference(copy,[status(thm)],[c_2736]) ).
cnf(c_2737,plain,
join(A,B) = join(A,join(A,B)),
inference(paramod,[status(thm)],[c_146,c_19]) ).
cnf(c_152,plain,
join(A,join(A,B)) = join(A,B),
inference(copy,[status(thm)],[c_2737]) ).
cnf(c_2738,plain,
composition(A,join(B,converse(C))) = join(composition(A,converse(converse(B))),composition(A,converse(C))),
inference(paramod,[status(thm)],[c_26,c_123]) ).
cnf(c_415,plain,
composition(A,join(B,converse(C))) = join(composition(A,B),composition(A,converse(C))),
inference(paramod,[status(thm)],[c_26,c_2738]) ).
cnf(c_2739,plain,
join(complement(join(A,B)),complement(A)) = join(complement(join(A,B)),complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_137,c_152]) ).
cnf(c_2740,plain,
join(complement(A),complement(join(A,B))) = join(complement(join(A,B)),complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_18,c_2739]) ).
cnf(c_527,plain,
join(complement(A),complement(join(A,B))) = complement(A),
inference(paramod,[status(thm)],[c_137,c_2740]) ).
cnf(c_543,plain,
join(complement(A),complement(join(B,A))) = complement(A),
inference(paramod,[status(thm)],[c_18,c_527]) ).
cnf(c_2741,plain,
join(A,complement(join(B,complement(A)))) = complement(complement(A)),
inference(paramod,[status(thm)],[c_96,c_543]) ).
cnf(c_564,plain,
join(A,complement(join(B,complement(A)))) = A,
inference(paramod,[status(thm)],[c_96,c_2741]) ).
cnf(c_2742,plain,
join(complement(complement(A)),complement(join(complement(join(A,complement(B))),complement(complement(join(A,B)))))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_137,c_139]) ).
cnf(c_2743,plain,
join(A,complement(join(complement(join(A,complement(B))),complement(complement(join(A,B)))))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_96,c_2742]) ).
cnf(c_2744,plain,
join(A,complement(join(complement(join(A,complement(B))),join(A,B)))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_96,c_2743]) ).
cnf(c_2745,plain,
join(A,complement(join(join(A,B),complement(join(A,complement(B)))))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_18,c_2744]) ).
cnf(c_2746,plain,
join(A,complement(join(A,join(B,complement(join(A,complement(B))))))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_19,c_2745]) ).
cnf(c_2747,plain,
join(A,complement(join(A,B))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_564,c_2746]) ).
cnf(c_622,plain,
join(A,complement(join(A,B))) = join(A,complement(B)),
inference(paramod,[status(thm)],[c_96,c_2747]) ).
cnf(c_2748,plain,
composition(A,join(B,C)) = join(composition(A,B),composition(A,converse(converse(C)))),
inference(paramod,[status(thm)],[c_26,c_415]) ).
cnf(c_2456,plain,
composition(A,join(B,C)) = join(composition(A,B),composition(A,C)),
inference(paramod,[status(thm)],[c_26,c_2748]) ).
cnf(c_2749,plain,
composition(A,top) = join(composition(A,B),composition(A,complement(B))),
inference(paramod,[status(thm)],[c_31,c_2456]) ).
cnf(c_2489,plain,
join(composition(A,B),composition(A,complement(B))) = composition(A,top),
inference(copy,[status(thm)],[c_2749]) ).
cnf(c_2750,plain,
join(complement(A),composition(sK0,top)) = join(composition(sK0,A),complement(A)),
inference(paramod,[status(thm)],[c_2489,c_121]) ).
cnf(c_2565,plain,
join(complement(A),composition(sK0,top)) = join(complement(A),composition(sK0,A)),
inference(paramod,[status(thm)],[c_18,c_2750]) ).
cnf(c_2751,plain,
join(complement(join(complement(A),composition(sK0,top))),complement(join(composition(sK0,A),complement(complement(A))))) = complement(composition(sK0,A)),
inference(paramod,[status(thm)],[c_2565,c_139]) ).
cnf(c_2752,plain,
join(complement(join(complement(A),composition(sK0,top))),complement(join(composition(sK0,A),A))) = complement(composition(sK0,A)),
inference(paramod,[status(thm)],[c_96,c_2751]) ).
cnf(c_2753,plain,
join(complement(join(complement(A),composition(sK0,top))),complement(join(A,composition(sK0,A)))) = complement(composition(sK0,A)),
inference(paramod,[status(thm)],[c_18,c_2752]) ).
cnf(c_2754,plain,
join(complement(join(complement(A),composition(sK0,top))),complement(A)) = complement(composition(sK0,A)),
inference(paramod,[status(thm)],[c_90,c_2753]) ).
cnf(c_2755,plain,
join(complement(A),complement(join(complement(A),composition(sK0,top)))) = complement(composition(sK0,A)),
inference(paramod,[status(thm)],[c_18,c_2754]) ).
cnf(c_2756,plain,
join(complement(A),complement(composition(sK0,top))) = complement(composition(sK0,A)),
inference(paramod,[status(thm)],[c_622,c_2755]) ).
cnf(c_2595,plain,
complement(composition(sK0,A)) = join(complement(A),complement(composition(sK0,top))),
inference(copy,[status(thm)],[c_2756]) ).
cnf(c_2757,plain,
meet(A,composition(sK0,top)) = complement(complement(composition(sK0,A))),
inference(paramod,[status(thm)],[c_2595,c_22]) ).
cnf(c_2758,plain,
complement(join(complement(A),complement(composition(sK0,top)))) = complement(complement(composition(sK0,A))),
inference(paramod,[status(thm)],[c_22,c_2757]) ).
cnf(c_2759,plain,
complement(join(complement(A),complement(composition(sK0,top)))) = composition(sK0,A),
inference(paramod,[status(thm)],[c_96,c_2758]) ).
cnf(c_2639,plain,
composition(sK0,A) = complement(join(complement(A),complement(composition(sK0,top)))),
inference(copy,[status(thm)],[c_2759]) ).
cnf(c_2760,plain,
( join(complement(complement(composition(sK0,sK1))),composition(sK0,sK1)) != complement(join(complement(sK1),complement(composition(sK0,top))))
| join(complement(join(complement(sK1),complement(composition(sK0,top)))),composition(sK0,sK1)) != composition(sK0,sK1) ),
inference(paramod,[status(thm)],[c_2595,c_43]) ).
cnf(c_2761,plain,
( join(composition(sK0,sK1),composition(sK0,sK1)) != complement(join(complement(sK1),complement(composition(sK0,top))))
| join(complement(join(complement(sK1),complement(composition(sK0,top)))),composition(sK0,sK1)) != composition(sK0,sK1) ),
inference(paramod,[status(thm)],[c_96,c_2760]) ).
cnf(c_2762,plain,
( composition(sK0,sK1) != complement(join(complement(sK1),complement(composition(sK0,top))))
| join(complement(join(complement(sK1),complement(composition(sK0,top)))),composition(sK0,sK1)) != composition(sK0,sK1) ),
inference(paramod,[status(thm)],[c_146,c_2761]) ).
cnf(c_2641,plain,
join(complement(join(complement(sK1),complement(composition(sK0,top)))),composition(sK0,sK1)) != composition(sK0,sK1),
inference(resolve,[status(thm)],[c_2639,c_2762]) ).
cnf(c_2763,plain,
join(complement(complement(composition(sK0,sK1))),composition(sK0,sK1)) != composition(sK0,sK1),
inference(paramod,[status(thm)],[c_2595,c_2641]) ).
cnf(c_2764,plain,
join(composition(sK0,sK1),composition(sK0,sK1)) != composition(sK0,sK1),
inference(paramod,[status(thm)],[c_96,c_2763]) ).
cnf(c_2765,plain,
composition(sK0,sK1) != composition(sK0,sK1),
inference(paramod,[status(thm)],[c_146,c_2764]) ).
cnf(c_2702,plain,
$false,
inference(copy,[status(thm)],[c_2765]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL026+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/10.38 % Computer : n006.cluster.edu
% 0.11/10.38 % Model : x86_64 x86_64
% 0.11/10.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/10.38 % Memory : 8046.5625MB
% 0.11/10.38 % OS : Linux 6.8.0-71-generic
% 0.11/10.38 % CPULimit : 300
% 0.11/10.38 % WCLimit : 300
% 0.11/10.38 % DateTime : Sat Sep 26 05:32:41 UTC 2026
% 0.11/10.38 % CPUTime :
% 0.11/10.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/10.38 % Process 465119 was started by sandbox2 on n006,
% 0.11/10.38 % Sat Sep 26 05:32:41 2026
% 0.11/10.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/10.39
% 0.11/10.39 % From the command line: assign(max_seconds, 300).
% 13.17/12.11
% 13.17/12.11 % SZS status Theorem for theBenchmark
% 13.17/12.11
% 13.17/12.11 % Proof 1 at 1.19 (+ 0.43) seconds.
% 13.17/12.11 % Length of proof is 70.
% 13.17/12.11 % Level of proof is 19.
% 13.17/12.11 % Maximum clause weight is 49.000.
% 13.17/12.11 % Given clauses 399.
% 13.17/12.11
% 13.17/12.11 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------